ECON455: Behavioral Economics

Q1: Insurance

Beth is taking ECON 455 and deciding when to study for the final exam versus relax. The final is on Saturday night, and Beth has come up with three possible plans:

Plan A: Attend the review session on Thursday, study on Friday, take the exam on Saturday

Plan B: Skip the review session on Thursday, study on Friday, take the exam on Saturday

Plan C: Skip the review session, relax on Friday, and take the exam without having prepared.

Beth's utility streams associated with each plan are described by the following table. Assume she starts evaluating plans at t=1.

A. Suppose Beth is an exponential discounter with δ = 0.5 and it's currently Thursday. Rank the plans in order of Beth's preference. Which plan will she choose?

B. Suppose Beth is a naive quasi-hyperbolic discounter with δ = 0.5 and β = 0.5 and it's currently Thursday. Rank the plans in order of Beth's preference. Which plan will she choose?

C. Suppose Beth is a naive type of the quasi-hyperbolic discounter and re-evaluates her plan on Friday, will she stick with her plan?

D. Suppose Beth is a sophisticated quasi-hyperbolic discounter with δ = 0.5 and β = 0.5 and it's currently Thursday. Rank the plans in order of Beth's preference. Which plan will she choose?

E. Suppose Beth is a sophisticated type of the quasi-hyperbolic discounter and re-evaluates her plan on Friday, will she stick with her plan?

F. Under what circumstances would the naive and the sophisticated type choose different plans, if given the choice to re-evaluate plans? Explain intuitively.

Q2: Seeking Alpha

Consider the decision to purchase health insurance. Imagine that there are three states of the world: you are in good health and spend $0 on healthcare; you are in fair health and spend $10,000 on healthcare; or you are in poor health and spend $100,000 on healthcare. The probability that you are in good health is 15%, the probability you are in fair health is 65% and the probability that you are in poor health is 20%. During open enrollment, you have to decide whether or not to buy insurance that will cover you next year. If you buy insurance, you are fully insured and you will pay nothing for healthcare.

If an economic agent believes that the current state of the world will persist into the future (possibly in opposition to probabilistic reality) we say they have a projection bias. This projection bias can be summarized via a parameter o. If o  1 for an economic agent this would mean they are certain the future state of the world will be identical to the present. If o - O they are certain that the current state of the world will not predetermine future states of the world in any way. For o between O and 1 we expect that there is o probability the future will be identical to the present and 1-a probability that future states of the world will be determined probabilistically (given the probabilities listed above). Assume that there is no actual correlation between your current health and your future health. Your happiness is associated with a utility function of the form. u(c) c, use this information to calculate the maximum amount of money you would be willing to pay for health insurance for the coming year in each of the following scenarios.

A. Imagine that you have a form. of projection bias. If α = 8/3 and your current health is poor, what is the maximum you are willing to pay for health insurance for the coming year?

B. Now imagine that you have the same form. of projection bias. If α = 8/3 and your current health is good, what is the maximum you are willing to pay for health insurance for the coming year?

C. Now imagine that you have an unknown degree of projection bias. If your current health is fair, what is the maximum o such that you will decide to purchase health insurance if it is being sold for $500?

D. Finally, imagine again that you have an unknown degree of projection bias. If your current health is good, what is the maximum o such that you will decide to purchase health insurance if it is being sold for $500?

Q3: Risk Premium and Certainty Equivalence

Jichael Mordan is famous for his love of gambling. His utility over money is U($) = $x$x$ = $3. That is to say his utility over money is the cube of however much money he has. Suppose Jichael is out golfing with his friend Bharles Carkley and currently has $3,000,000.00 in his wallet. Bharles offers Jichael a $2,000,000.00 bet on the flip of a fair coin: 50% probability he loses $2,000,000.00 (walks away with $1,000,000.00) and 50% probability he wins $2,000,000.00 (walks away with $5,000,000.00). Use this information to answer the following:

A. Plot Jichael's Bernoulli utility function. Is Jichael risk-loving, risk-averse, or risk-neutral?

B. Will Jichael take this bet? Show that his expected utility is higher/lower if he accepts/declines this gamble. Mark the expected utility of the gamble on the graph from (A).

C. What is the expected value of this gamble? Mark this number on the graph from (A).

D. How much money will make Jichael indifferent between taking the gamble or walking away (what is the certainty equivalent of this gamble)? Is it greater or smaller than the expected value of the lottery? Write an economic interpretation of this number.

Q4: Popping

Suppose that agents live for three periods: youth, middle age, and old age. In each period, agents choose whether to consume an addictive substance (to pop) or to refrain. Once an agent pops they cannot stop, meaning trying the substance causes addiction in ALL future periods. Now further suppose the benefit from "popping" varies across periods and is decreasing over time. In other words, consuming the addictive substance is more tempting when one is young. Let Uy represent utility during youth, Um be utility during middle age, and Uo be utility during old age. The utility associated with several states of the world are summarized here:

A. If δ = 1, in what periods will a time-consistent economic agent who enters youth not "popping" choose to pop? Prove this is the agent's optimal consumption path.

B. If δ = 1 and β = 2/1, in what periods will a naive agent who enters youth not addicted choose to pop?

C. If δ = 1 and β = 2/1,in what periods will a sophisticated agent who enters youth not addicted choose to pop?

D. Discuss the behavioral implications of your answers in parts (A)-(C). How does the behavior. of different types impact the outcome of their rational decisions?

Q5: Dating

L is amazing. You are considering asking L out for a date but you are more than a little worried that L is dating somebody else. You figure the probability that L is dating somebody else is one chance in three. If L is dating somebody else, he/she is unlikely to accept your offer to go on a date: in fact, you think the probability is only one in five-hundred chance that they will accept if they are dating someone else. If L is not dating somebody else, you think the probability is one chance in one-hundred that they will accept your offer. Use this information to answer the following, using explicit notation in your calculations and complete sentences to explain your logic. Incomplete or inarticulate responses will not earn credit for this grade item.

A. What is the probability that L is dating somebody else but will accept your offer to go on a date anyway?

B. What is the probability that L is not dating somebody else and will accept your offer to go on a date?

C. What is the probability that L will accept your offer to go on a date?

D. Suppose L accepts your offer to go on a date. What's the probability that L is dating somebody else, given that L agreed to go on a date?